I DO want to be able to say I 'fire blued' the barrel,
OK dude, here's the downside. If you use the pit method, you have no control over the color. From the time you put the barrel in to the time the fire goes out and it has cooled in the ashes, you really can't see what is happening, although you can remove the lid and look. But then you have to re-regulate the temp. Temp is regulated by pine splinter....see next para.
Everything has to be highly polished for best results. For the forge or stove methods, there are alternatives. You can use sand, finely ground charcoal, or wood ashes in a metal box on top of the forge. The sand should be white silica sand as used in sandblasting. You buy it in 100 lb bags. The charcoal must be pure wood charcoal, not bound briquets.
You build your fire and uniformly heat your media, stirring it while heating. When it will just ignite a large pine splinter, it's ready. Bury your barrel in the media. Have a polished piece of steel to lay on top. When the top piece hits the color you want, remove the barrel and heavily oil it to stop the action.
The last method involves only a heavy steel plate on the forge/fire. Lay the plate over the fire with the barrel on it. Everything will heat up together and go thru the changes. When the barrel hits the color you want, take it off and rub with heavy oil to stop the action. This is probably the simplest method.
Lastly, I think the color that you are looking for is the pale blue. I have looked at my sources because I remember the term "water blue." However, I have not been able to find the method to achieve it. I do recall that the color only occurs very briefly as a transitional phase at a very narrow temperature range.
Again, you want your barrel to be mirror bright.
Gud Luk